This invention relates generally to the art of recording and displaying electrical waveforms, and more specifically, to the art of reconstructing and displaying a waveform from a minimum number of sample data points of an actual analog waveform.
There are a number of types of instruments that digitize and store samples of an analog waveform and display on a CRT or other graphic display device a reconstruction of the analog signal that produced those samples. Instruments that use this technique include transient analyzers, waveform recorders and digital oscilloscopes. There are often very few samples taken per cycle of the waveform being analyzed, either because the frequency of the waveform approaches one-half the maximum sampling rate of the instrument or because the user selects a low sampling rate which enables the limited memory of the instrument to store samples over a longer time interval. Pursuant to the well known Nyquist theorem, at least two samples must be taken for each cycle of the analog waveform in order to permit its reconstruction.
If there are only a few samples per cycle of the waveform, the display of those samples alone will not give enough information for the viewer to adequately visualize the original analog waveform. One common aid to visualization is to connect the dots with straight lines but this can give an inaccurate representation of the original waveform if there are few samples per cycle, which is often the case.
A more sophisticated approach to reconstructing a replica of the original waveform is to perform a filtering or Fourier operation on a string of samples taken of the magnitude of the original waveform. This provides a much better visualization of the analog signal and can be implemented in either dedicated hardware, such as a digital-to-analog converter followed by a transversal filter, or in software if the instrument is microprocessor or computer based. However, the hardware approach is expensive and the software approach has a disadvantage of requiring a large number of high precision multiply and divide operations which takes a considerable amount of time.
Another software approach has also been used when there are a significant number of samples per cycle in excess of the minimum two samples. The slopes of the waveform at each sampled point are first roughly estimated using only the data points immediately on either side of each point, and then one of a number of stored display segments having the closest match of its end point slopes is selected from a number of such stored display segments, which may be 50 or more in number. This technique has a disadvantage of having lesser accuracy than other techniques when few samples per cycle exist.
Therefore, it is a principal object of the present invention to provide a technique and system for accurately, rapidly and inexpensively reconstructing analog waveforms from a series of magnitude samples of an actual analog waveform.